Solve frac{sqrt{972}}{sqrt{64}}286

$$\frac{ \sqrt{ 972 } }{ \sqrt{ 64 } } 286$$

Evaluate

$$\frac{1287\sqrt{3}}{2}\approx 1114.574694671$$

Solution Steps

Factor 972=18^{2}\times 3. Rewrite the square root of the product \sqrt{18^{2}\times 3} as the product of square roots \sqrt{18^{2}}\sqrt{3}. Take the square root of 18^{2}.

$$286\times \frac{18\sqrt{3}}{\sqrt{64}}$$

Calculate the square root of 64 and get 8.

$$286\times \frac{18\sqrt{3}}{8}$$

Divide 18\sqrt{3} by 8 to get \frac{9}{4}\sqrt{3}.

$$286\times \frac{9}{4}\sqrt{3}$$

Express 286\times \frac{9}{4} as a single fraction.

$$\frac{286\times 9}{4}\sqrt{3}$$

Multiply 286 and 9 to get 2574.

$$\frac{2574}{4}\sqrt{3}$$

Reduce the fraction \frac{2574}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1287}{2}\sqrt{3}$$